1. Field
The present disclosure relates to calibration of inter-channel bias in navigation satellite systems.
2. Related Art
Navigation receivers that utilize the signals of the global navigation satellite systems GPS and GLONASS enable various positioning tasks with very high accuracy. A GPS or GLONASS receiver receives and processes radio signals transmitted by the navigation satellites. The satellite signals are carrier harmonic signals that are modulated by pseudo-random binary codes which, on the receiver side, are used to measure the delay relative to a local reference clock. These delay measurements are used to determine the so-called pseudo-ranges between the receiver and the satellites. The pseudo-ranges are different from the true geometric ranges because the receiver's local clock is different from the satellite onboard clocks. If the number of satellites in sight is greater than or equal to four, then the measured pseudo-ranges can be processed to determine the user's single point location X=(x, y, z)T (all vectors are represented as columns; the symbolT denotes matrix/vector transpose), as well as compensate for the receiver clock offset.
The necessity to improve positioning accuracies has eventually led to the development of “differential navigation/positioning.” In this mode, the user position is determined relative to the antenna connected to a Base receiver, assuming that the coordinates of the Base are known with high accuracy. The Base receiver will transmit its measurements (or corrections to the full measurements) to a mobile navigation receiver (“Rover”). The Rover receiver will use these corrections to refine its own measurements in the course of data processing. The rationale for this approach is that since most of the pseudo-range and pseudo-phase measurement errors on the Base and Rover sides are strongly correlated, using differential measurements will substantially improve the positioning accuracy.
The fundamental task of a GPS or GLONASS receiver is to measure distances to several GPS or GLONASS satellites and compute receiver coordinates. Distances are measured to satellites by measuring the travel time of signals from the satellites to the core of the receiver electronics where the received signals are processed. Data used from a Base receiver (at a known point) removes common errors in the Rover and yields accurate results. The signal path from each satellite to the receiver electronics consists of two parts: 1) the direct path in space from the satellite to the receiver antenna, and 2) from the receiver antenna to the receiver electronics. The first path is unique to each satellite. The second path is common for all satellites, and is where the signal travels through antenna electronics, antenna cable, and to the analog and digital sections of the receiver. The signal travel time through the second path is referred to as the “receiver bias.” As long as the receiver bias is the same for all satellites, it acts as a component of the receiver clock offset, which we solve as the fourth unknown (along with x, y, z). In other words, if the receiver bias is the same for all satellites it does not impact position computations.
However, the receiver biases for all GLONASS receivers are not the same. The reason is that the receiver bias, or group delay, depends on the satellite signal frequency and that GLONASS satellites transmit on different frequencies. As a result, each GLONASS satellite generates a different receiver bias. In technical terminology, GLONASS satellites cause inter-channel biases which, if not taken into account, can significantly degrade position accuracy. Fortunately, all common errors between the Base and the Rover receivers are cancelled. Therefore, if the magnitudes of the GLONASS inter-channel biases in the Base receiver and in the Rover receiver are the same, these biases will be cancelled and they will not degrade the position accuracy. However, this rarely happens. This is due to the fact that the magnitudes of the inter-channel biases depend not only on the receiver design and its electronic components, but also on the temperature and slight variations in the electronic components. Even in the best case where the Base and the Rover receivers are from the same manufacturer and have identical design, components, and manufacturing dates, there is still the issue of temperature and minute component differences. The magnitude of the GLONASS inter-channel biases can prohibit the use of GLONASS satellites for precision applications.
While GPS satellites transmit on the same frequency, the receiver biases generated by the satellites may still be different. This may occur due to slight differences in the frequencies of the satellite signals caused by different Doppler shifts as the satellites orbit around Earth. In some examples, a frequency difference of up to 10 KHz may result from the different Doppler shifts. Additionally, similar to GLONASS receivers, the inter-channel bias of a GPS receiver depends on temperature and slight variations in electronic components.
When the objective is to achieve centimeter and sub-centimeter accuracy, dealing with GPS and GLONASS inter-channel biases is not an easy task. Currently, some manufacturers simply ignore the inter-channel biases. When the inter-channel biases are noticeable, one solution is to use GPS and GLONASS to resolve ambiguities, and then ignore one of the GPS or GLONASS measurements or significantly de-weight them. Dealing with the problem in this manner does not allow the user to know why their GPS+GLONASS receiver does not show any improvement over GPS-only or GLONASS-only receivers. When the receiver firmware cannot isolate the GPS or GLONASS satellites with high inter-channel biases it provides inaccurate results. This is a serious problem that causes the user to accept faulty results. Other manufacturers try to measure the GPS or GLONASS inter-channel biases in a sample of pre-production receivers and hardcode these biases into the firmware. This is a positive step forward but by no means can cure the problem because there are still differences between electronic components compared to the sample, and their characteristics vary by temperature and time.
Thus, a solution is needed to dynamically account for and calibrate receiver specific inter-channel biases.